Re: Strange behaviour of Plot
- To: mathgroup at smc.vnet.net
- Subject: [mg107667] Re: Strange behaviour of Plot
- From: dh <dh at metrohm.com>
- Date: Mon, 22 Feb 2010 08:31:13 -0500 (EST)
- References: <hlj43f$rt6$1@smc.vnet.net>
Hi, your function contains an If statement. Therefore, you can not expect the function to be continuous. Consider e.g. Summand2 for m=0; If[j == m, 0, 2/((j - m)^2 \[CapitalDelta]^2) (-3 + Exp[-(((j - m)^2 \[CapitalDelta]^2)/2)] (3 + 2 (j - m)^2 \[CapitalDelta]^2))] /. m -> 0 gives: If[j == 0, 0, ( 2 (-3 + Exp[-(1/2) ((j - 0)^2 \[CapitalDelta]^2)] (3 + 2 (j - 0)^2 \[CapitalDelta]^2)))/((j - 0)^2 \[CapitalDelta]^2)] clearly this is not continuous at m=0. Due to finite resolution, the plot routine ignores (does not find) these singular points. Daniel On 18.02.2010 11:17, Very Bad Mother... wrote: > Hi, > I've found it quite puzzling. Pls, have a look. > I define the following functions: > > Summand2[j_, m_, \[CapitalDelta]_] := > If[j == m, 0, > 2/((j - m)^2 \[CapitalDelta]^2) (-3 + > Exp[-(((j - m)^2 \[CapitalDelta]^2)/2)] (3 + > 2 (j - m)^2 \[CapitalDelta]^2))]; > > sigma[m_, Nm_, \[CapitalDelta]_] := NSum[Summand2[j, m, \ > [CapitalDelta]], {j, 0, Nm - 1}]; > > where j and m are supposed to be integers and \[CapitalDelta] to be a > "double" (in C-terms). > Now, I'd like to plot the sigma function: > Plot[sigma[m, 4, 6], {m, 0, 3}] > So, ofcourse, I obtain a plot of a continues function, for all ms > between 0 and 3. From this plot one can find that the values of sigma > for integers are positive and about 0.6. However, what is interesting, > if one evaluates explicitly sigma[m, 4, 6] for m=0, 1, 2, 3, one will > find that actually the values are negative about -0.3. > How is that possible? It's really confusing. Any help appreciated. > Thank you in advance, > -- > Kind regards, > tinkerbell > -- Daniel Huber Metrohm Ltd. Oberdorfstr. 68 CH-9100 Herisau Tel. +41 71 353 8585, Fax +41 71 353 8907 E-Mail:<mailto:dh at metrohm.com> Internet:<http://www.metrohm.com>